Abstract

A subgroup H of a group G is called malnormal in G if it satisfies the condition that if g∈G and h∈H, h≠1
such that ghg−1∈H, then g∈H. In this paper, we show
that if G is a group acting on a tree X with inversions such
that each edge stabilizer is malnormal in G, then the
centralizer C(g) of each nontrivial element g of G is in a
vertex stabilizer if g is in that vertex stabilizer. If g is
not in any vertex stabilizer, then C(g) is an infinite cyclic
if g does not transfer an edge of X to its inverse. Otherwise,
C(g) is a finite cyclic of order 2.

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